16. Decide whether b is in the subspace spanned by w1, W2, W3, where wų =...
Let W be the subspace spanned by the given vectors. Find a basis for Wt, 0 1 A. W1 = W2 = 3 2 -1 2 B. W W2 2 -3 W3 = 6
5 3 1 0 Problem 10 Let wi = ,W2 W3 Let W = Span{W1,W2, W3} C R6. 11 9 1 2 a) [6 pts] Use the Gram-Schmit algorithm to find an orthogonal basis for W. You should explicitly show each step of your calculation. 10 -7 11 b) [5 pts) Let v = Compute the projection prw(v) of v onto the subspace W using the 5 orthogonal basis in a). c) (4 pts] Use the computation in b) to...
Let B = [V1, V2, V3] and B' = [W1, W2, W3] be bases for a vector space V and Vi = W1 + 5W2 – W3 U2 = W1 U3 -W1 - 4w2 – 2w3 If (U)b = (1,-1,2), then the coordinates of v relative to the basis B' are c1 = C2 = and cz
An experiment has four outcomes O1,O2,O3, and O4 with corresponding weights w1,w2,w3, and w4 where w1=7/k, w2=7/k,w3=6/k, and w4=1/k. What is the value of k? What is Pr({O1,O4})?
Jones company has two manufacturing plants A and B, and three warehouses, W1, W2, W3. Each week Jones ships product from the plants to the warehouses. The system is balanced: A produces 500 units of product and B produces 300 units of product. Warehouse W1 needs 200 units of product, W2 needs 300 units of product, and W3 needs 300 units of product. Thus, over the entire system, there are 800 units produced by the two plants and 800 units...
hint: H3. Let W1 = {ax? + bx² + 25x + a : a, b e R}. (a) Prove that W is a subspace of P3(R). (b) Find a basis for W. (c) Find all pairs (a,b) of real numbers for which the subspace W2 = Span {x} + ax + 1, 3x + 1, x + x} satisfies dim(W. + W2) = 3 and dim(Win W2) = 1. H3. (a) Use Theorem 1.8.1. (b) Let p(x) = ax +...
5. Given a linear map f R3R3 if V Vi, V2, va) is a basis of R3, and further, a) State the defining matrix of f under the basis vi, V2, vs) -3 2 0 b) Let W-(w1, w2, w3) be another basis of R3 and P42 be the change- 01-1 of-coordinate matrix from V to W. Let A be the defining matrix for f under the basis W diagonalize A. 5. Given a linear map f R3R3 if V...
When w1 = 10 kN/m, w2=8 kN/m, w3 = 2 kN/m, a = 3 m and b = 3 m for the system shown below, determine the internal moment in kN.m at a section passing through point C. Thereafter, choose the correct answer from the values provided below.
2. Let Wi-((a, b, c) : a-c-b), W2-((a, b, c) : ab>0), W3-((z, y,z) : r2+92+22£1} be subsets of R3 (a) Determine which of these subsets is a subspace of R3. Justify your answer. (b) For the subsets which are subspaces, find a basis and the dimension for each of them 2. Let Wi-((a, b, c) : a-c-b), W2-((a, b, c) : ab>0), W3-((z, y,z) : r2+92+22£1} be subsets of R3 (a) Determine which of these subsets is a subspace...
what is w1 and w2 in quetion b and c .. where these numbers pluged for W1 and W2 came from ? Question CS You are thinking of investing in shares in Grev Matter Ltd. The possible returns on Grey Matter shares over the next year, and the probability of three of those returns, are shown in the following table. Probability 8 % Return -4 % Yound to l00 28% 3% 40 % 8 % 13% Ki-001-(oht8+3 Jusi [2 marks]...